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Proof step 3 from proof ubifs-log-nodups-add4 (previous step)

dups(log + adr0 ' + adr1 ' + adr2 ' + adr3 '), ubifs-cons(fs, ri, ro, fi, fo, log) ⊦ adr0 = adr1, adr0 = adr2, adr0 = adr3, adr1 = adr2, adr1 = adr3, adr2 = adr3, adr0 ∈ fs, adr1 ∈ fs, adr2 ∈ fs, adr3 ∈ fs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ↔ ¬ inodekey(0) ∈ ri ∧ ri-cons(ri, fs) ∧ log-cons(log, fs) ∧ ¬ dups(log) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? ∧ fo.inodes? ∧ ro ⊆ dom ri ∧ fo ⊆ dom fi
Proof step 5:
ro.inodes?, fo.inodes?, dups(log + adr0 ' + adr1 ' + adr2 ' + adr3 '), log-cons(log, fs), ri-closed(ri, fs, ro), ri-cons(ri, fs), ro ⊆ dom ri, fo ⊆ dom fi ⊦ adr0 = adr3, adr0 = adr2, adr0 = adr1, adr1 = adr3, adr1 = adr2, adr2 = adr3, dups(log), adr3 ∈ fs, adr2 ∈ fs, adr1 ∈ fs, adr0 ∈ fs, inodekey(0) ∈ ri

Rule argument

spec: <toplevel> name: ubifs-cons seq: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ↔ ¬ inodekey(0) ∈ ri ∧ ri-cons(ri, fs) ∧ log-cons(log, fs) ∧ ¬ dups(log) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? ∧ fo.inodes? ∧ ro ⊆ dom ri ∧ fo ⊆ dom fi subst: [log, fo, fi, ro, ri, fs] → [log, fo, fi, ro, ri, fs] flags: <all paths>

Additional information

Used terms: log, fo, fi, ro, ri, fs